Answer
$27y^\frac{2}{3}$
Work Step by Step
$$\frac{(3y^\frac{1}{4})^3}{y^\frac{1}{12}}$$
When an exponential expression is raised to a power, multiply the exponents:
$$=\frac{27y^{(\frac{1}{4} \times 3)}}{y^\frac{1}{12}}$$
$$=\frac{27y^\frac{3}{4}}{y^\frac{1}{12}}$$
When exponential expressions with the same base are divided, subtract the exponent of the denominator from the exponent of the numerator:
$$=27y^{(\frac{3}{4}-\frac{1}{12})}$$
To subtract fractions, you need a common denominator; in this case, 12:
$$=27y^{(\frac{9}{12}-\frac{1}{12})}$$
$$=27y^{\frac{8}{12}}$$
Simplify all fractions:
$$=27y^\frac{2}{3}$$
